[Proof of Theorem 1]
For completeness, first note that measurability issues and non-emptyness
of \(\Theta _{0}\)  and \(\hat{\Theta }_{n}\)  (with probability one) are
discussed in [1]}. For ease
of reference, also note that for any two bounded real-valued functions
\(u\)  and \(v\)  defined on a domain \(D\)  (a subset of some Euclidean
space),
\(| \sup u(x)-\sup v(x) | \le \sup | u(x)-v(x) |,\;\;\:| \inf u(x)-\inf v(x) | \le \sup | u(x)-v(x) | , \) 
